Let be the size of the mincut of G. Let p = min(1,10lnn), and let H = (V,E) be a random subgraph of G where each edge of G remains in H independently with probability p. Prove that H remains connected with probability at least 1 n(1). Hint: Given S V , what is the probability that no edge from S is sampled? You might want to do a smart union bound depending on |S|